A method for increasing the number of multiplexing channels of non-interleaved multi-dimensional channel multiplexing metasurface

Abstract

The present invention discloses a method for increasing the number of multiplexed channels in a non-interleaved multidimensional channel multiplexing metasurface. Using a GS algorithm optimized based on the first-kind Rayleigh-Sommerfeld formula, the phase distribution information required for the target metasurface can be obtained. Using the dispersive Jones matrix and gradient descent method, multiple phase distribution information can be optimized into the required metaatom information, which is then compared with the metaatom phase database to ultimately form the target metasurface. The non-interleaved metasurface produced by the method of the present invention can be expanded to three dimensions: wavelength, polarization state, and diffraction distance. It can also simultaneously utilize three polarization channels, three wavelength channels, and two reconstruction distances, increasing the number of multiplexed channels to 18.

Description

Technical Field

[0001] The present invention relates to metasurface technology, specifically a method for increasing the number of multiplexed channels in a non-interleaved multidimensional channel multiplexing metasurface based on the dispersion Jones matrix, the first-kind Rayleigh-Sommerfeld diffraction formula, the GS algorithm, and the gradient descent method. This method can be used to design non-interleaved metasurfaces for multidimensional channel multiplexing, increasing the number of multidimensional multiplexing channels that can be implemented on the metasurface. Background Art

[0002] A metasurface is a two-dimensional device composed of subwavelength nanounits arranged in a regular pattern. It can manipulate the phase, amplitude, and polarization state of electromagnetic waves with extremely high precision. Compared to the bulky and heavy traditional optical devices, metasurfaces offer advantages such as small size, low weight, low cost, multifunctionality, and ease of integration. Metasurfaces are used to achieve multi-dimensional channel multiplexing, and holographic imaging is achieved through metasurface holography. The core of this method lies in the use of metaatoms to manipulate the physical parameters of light in multiple dimensions, such as polarization, wavelength, orbital angular momentum, and imaging distance. This allows a single metasurface to reproduce a large number of holographic images, thereby increasing the device's optical information storage density. This is of great significance and value for meeting the practical needs of future optical color imaging, optical encryption, information storage, and transmission.

[0003] Currently proven metasurface design methods primarily increase the number of reusable channels by designing interleaved and non-interleaved metasurfaces. Interleaved metasurfaces achieve a greater degree of freedom by combining multiple metaatoms into a single unit. Each metaatom within a unit can independently manipulate light waves of different wavelengths or polarizations based on its physical properties. When a light wave passes through a unit, it is independently manipulated by different metaatoms, ultimately synthesizing the desired outgoing light wave, which serves as a pixel on the metasurface holographic image. This design approach is simple and intuitive, but overly large units can reduce periodicity and the quality of the reconstructed image. Non-interleaved metasurfaces combine the limited degrees of freedom of the metaatoms with physical dimensions such as the wavelength, polarization, and holographic image reconstruction distance to achieve multi-dimensional channel multiplexing. However, existing design methods are not ideal for designing in two or more dimensions. For example, they either utilize only one or two of the wavelength, polarization, topological charge, and holographic image reconstruction distance dimensions, or utilize all three dimensions but only provide two polarization channels. This leaves room for further increasing the number of reusable channels. The present invention provides a novel method for inverse design of non-staggered metasurfaces. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for increasing the number of multiplexed channels of a non-interleaved multidimensional channel multiplexing metasurface, mainly to solve the technical problem of the small number of multiplexed channels in existing methods. It uses the dispersion Jones matrix to control the perfectly isolated polarization channels at different wavelengths, optimizes the known GS algorithm and gradient descent method through the first-class Rayleigh-Sommerfeld formula to reversely design the metasurface, and explores the application potential of the reconstruction distance variable. Ultimately, it can realize multidimensional channel multiplexing of three polarization channels, three wavelength channels and two reconstruction distances, expanding the number of multiplexed channels to 18.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface, characterized in that it comprises:

[0007] The traditional GS algorithm is optimized using the first-kind Rayleigh-Sommerfeld diffraction formula. This optimization method regards the diffraction process as a response process and extracts the response function from the first-kind Rayleigh-Sommerfeld diffraction formula, and then performs iterative calculations.

[0008] The ability of meta-atoms on the metasurface to control the light field can be expressed using the Jones matrix To describe it, when the superatom rotates, the Jones matrix becomes

[0009]

[0010] After processing the target image with the optimized GS algorithm, the phase distribution information required for designing the metasurface can be obtained. Then, the phase distribution information is processed by the Jones matrix and gradient descent method to obtain the phase Ψ related to the specific metaatom. x , Ψ y and the information distribution of the rotation angle θ, and the superatom Ψ x , Ψ y The phase database is compared to obtain the required meta-atom and finally the target metasurface.

[0011] The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface is characterized by:

[0012] The response function extracted from the first kind of Rayleigh-Sommerfeld diffraction formula is The Rayleigh-Sommerfeld formula of the first kind becomes U=F -1 {F{U0}F{h}}, in order to ensure the iteration is valid, the inverse diffraction needs to be changed to

[0013]

[0014] The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface is characterized by:

[0015] Jones Matrix The elements of the Jones matrix represent polarization channels. To ensure that the energy of each channel is uniform, that is, the amplitude of all channels is the same, the Jones matrix is ​​restricted to Ψ1, Ψ2 and Ψ3 are about Ψ x , Ψ y and the function of the rotation angle θ.

[0016] The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface is characterized by:

[0017] The loss function of the gradient descent method is: Δ i is the difference between the target value and the calculated value.

[0018] The method of the present invention has the following advantages:

[0019] 1. The method of the present invention adopts the first kind of Rayleigh-Sommerfeld formula as the diffraction formula and optimizes the traditional GS algorithm, resulting in better imaging effect;

[0020] 2. The method of the present invention utilizes the gradient descent method to optimize parameters, and the optimization and convergence speeds are fast.

[0021] 3. Using the method of the present invention, a non-interlaced metasurface with a large number of reusable multi-dimensional channels can be produced, which effectively increases the number of channels of the non-interlaced metasurface device.

[0022] 4. The method of the present invention is simple and direct. The subsequent simulation examples prove the effectiveness and reliability of the method and have practical engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Schematic diagram of a supercell and a supersurface provided by an embodiment of the present invention;

[0024] Figure 2 is a phase database of an embodiment of the present invention;

[0025] Figure 3 is a flow chart of an embodiment of the present invention;

[0026] Figure 4 It is an iterative cycle diagram of the optimized GS algorithm of the present invention;

[0027] Figure 5 is a Loss curve diagram of the gradient descent algorithm provided by an embodiment of the present invention;

[0028] Figure 6It is a schematic diagram of the results of a holographic imaging experiment with three polarization channels, three wavelength channels, and double diffraction distances in a non-interlaced metasurface inverse design method provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The present invention discloses a method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface, which specifically comprises the following steps:

[0030] Step 1: Use the first kind of Rayleigh-Sommerfeld formula to optimize the traditional GS algorithm. The first kind of Rayleigh-Sommerfeld formula is as follows:

[0031]

[0032] Where r is the distance between the reconstructed light field and the metasurface. The process of reconstructing the light field is regarded as a response process, and the response function is The Rayleigh-Sommerfeld formula of the first kind becomes U=F -1 {F{U0}F{h}} can be brought into the GS algorithm for iterative calculation. In order to ensure that the iteration is valid, it is necessary to make The optimized GS algorithm is obtained. Since the first-kind Rayleigh-Sommerfeld formula includes parameters such as light wavelength and diffraction distance, different wavelengths and diffraction distances can be set in this step, assigning the target image to different wavelength channels and diffraction distances, achieving multiplexing in both wavelength and diffraction distance dimensions. Finally, the intensity map of the target image and the intensity of the incident light are fed into the optimized GS algorithm to obtain the phase distribution information required to design the metasurface.

[0033] Step 2: Use the Jones matrix to realize the polarization state channel allocation. The meta-atom used is a cubic structure. When the meta-atom does not rotate, the outgoing light generated by the incident light passing through the meta-atom can be expressed by the following Jones matrix:

[0034]

[0035] where Ψ x and Ψ y They are the phase shifts of x-polarized light and y-polarized light respectively when they pass through a superatom with a rotation angle of 0. When the superatom has a rotation angle θ, the Jones matrix will become Where R(θ) is the rotation matrix. Since the present invention includes more than two polarization channels, it is necessary to ensure that the energy of each channel is uniform, that is, the amplitude of all channels is the same, so the above Jones matrix needs to be limited to , Ψ1, Ψ2 and Ψ3 are about Ψ x , Ψ y As a function of the rotation angle θ, the relationship between the incident light and the outgoing light can be described as E o =J θ ·Ein Phase Ψ1 corresponds to the x-polarization -> x-polarization channel, phase shift Ψ2 controls the x-polarization -> y-polarization / y-polarization -> x-polarization cross-polarization channel, and phase shift Ψ3 controls the y-polarization -> y-polarization channel. By matching the phase distribution information obtained in step 1 with Ψ1, Ψ2, and Ψ3, the target image can be assigned to a specific polarization channel.

[0036] Step 3: Use the gradient descent method and Ψ1, Ψ2, Ψ3 about Ψ x , Ψ y , the function of the rotation angle θ, and the phase Ψ associated with the specific superatom is obtained. x , Ψ y The phase distribution information is used as Ψ1, Ψ2 and Ψ3 in the function, and Ψ x , Ψ y and the rotation angle θ are set as optimization variables, and the loss function Loss is used i :

[0037]

[0038] Among them, Δ i is the difference between the target value and the calculated value. Since the elements in the Jones matrix represent the light field, the target light field p can be obtained. i and the calculated light field When calculating the loss function, the two light fields need to be split into real parts Re(p i ), and the imaginary part Im(p i ), Difference Δ i Also divided into and There are two types, and the corresponding loss function is Loss i-1 and Loss i-2 , the overall loss function is In order to ensure the efficiency of calculating the differentials of multiple variables, the present invention uses PyTorch to implement the gradient descent method, and finally obtains Ψ x , Ψ y and the phase distribution of the rotation angle θ.

[0039] Step 4: Use FDTD commercial software to scan the designed superatom to obtain the Ψ that superatoms of different sizes can produce. x , Ψ y , and the obtained metasurface Ψ x , Ψ y The phase distribution is compared and selected to obtain the required meta-atom, and finally the required metasurface is designed based on the phase distribution of the rotation angle θ.

[0040] Example

[0041] In order to better understand the process, purpose and advantages of the present invention, the method of the present invention will be described in detail below with reference to the accompanying drawings.

[0042] Step 1: First, we need to scan and obtain the Ψ that can be produced by superatoms of different sizes. x , Ψ y In this case, the operating wavelengths of light waves are 3.5μm, 4μm, and 4.5μm, the materials of the superatom and the substrate are Si, and the geometric shape of the superatom is a cube, such as Figure 1 As shown, the period P = 1.8 μm, the height H = 7 μm, and the length and width range from 200 nm to 1200 nm. The length and width of the meta-atom were measured at 50 points at equal intervals, for a total of 2500 meta-atoms of varying geometric dimensions. The meta-atoms were illuminated with linearly polarized light of three target wavelengths, with x- and y-polarizations, respectively, to demonstrate their ability to manipulate light at wavelengths of 3.5 μm, 4 μm, and 4.5 μm. Figure 2 The three pictures above are superatomic Ψ x Database, the three pictures below are y Database. In each database, x , Ψ y All achieve full coverage from -π to +π and phase shift Ψ at the same wavelength x , Ψ y Furthermore, light waves of different wavelengths have different phase shifts with respect to the same meta-atom, indicating that a single meta-atom can simultaneously manipulate light waves of different wavelengths, achieving dispersion holography.

[0043] Step 2: Apply the optimized GS algorithm for iterative calculation to obtain the phase distribution information of each target pattern. The metasurface of this implementation case is designed as a non-interlaced metasurface with a pixel size of 250×250 (450μm×450μm). First, the target patterns need to be distributed according to the wavelength and diffraction distance. The digital images "1" to "9" are planned to be reproduced on the focal plane at 250μm from the metasurface, and the uppercase letter images "A" to "I" are planned to be reproduced on the focal plane at 650μm. Images "1", "2", "3", "A", "B", and "C" are reconstructed using light waves with a wavelength of 3.5μm, "4", "5", "6", "D", "E", and "F" are reconstructed using light waves with a wavelength of 4μm, and "7", "8", "9", "G", "H", and "I" are reconstructed using light waves with a wavelength of 4.5μm. Then the distance parameters and wavelength parameters corresponding to each target image are substituted into the first-class Rayleigh-Sommerfeld formula to obtain the corresponding response function. Finally, according to the following Figure 4The optimized GS algorithm shown in FIG5 is used for iterative calculation to obtain the required phase distribution information.

[0044] Step 3: Assign the target image to different polarization channels according to Ψ1, Ψ2, and Ψ3. x , Ψ y , a function of the rotation angle θ, and applying the gradient descent method, we can get the Ψ required for selecting the unit. x , Ψ y , the rotation angle θ distribution information. Assign images "1", "4", "7", "A", "D", and "G" to the x-polarization-x-polarization state channel, and images "2", "5", "8", "B", "E", and "H" to the x-polarization-y-polarization / y-polarization-x-polarization cross channel, and "3", "6", "9", "C", "F", and "I" to the y-polarization-y-polarization channel. Substitute the data of each channel into the corresponding Ψ1, Ψ2, and Ψ3 functions, and convert Ψ x , Ψ y and the rotation angle θ are set as optimization variables, and the gradient descent method is used for optimization. The descent curve of the loss function is as follows: Figure 5 As shown, the desired Ψ can be obtained x , Ψ y and the rotation angle θ distribution information.

[0045] Step 4: According to the obtained Ψ x , Ψ y And the rotation angle θ distribution information is used to select super atoms and form a super surface. x , Ψ y The phase distribution information is respectively related to the phase shift Ψ of the corresponding wavelength x , Ψ y The database is compared, that is, for a certain pixel point, the corresponding phase shift Ψ x , Ψ y It is transformed into a complex function form and subtracted from the data in the database to obtain the modulus. Since there are multiple Ψ x , Ψ y , we need to add their results and take the minimum value to find the most suitable meta-atom. After obtaining the required meta-atom, combined with the information of the rotation angle θ distribution, we can design the required meta-surface. The holographic imaging results of the three-polarization channel, three-wavelength channel, and double diffraction distance achieved by the non-interlaced meta-surface designed in this embodiment are as follows: Figure 6 As shown, on the focal plane of f=250 μm, nine digital patterns from “1” to “9” are reproduced, and on the focal plane of f=650 μm, nine capital letter patterns from “A” to “I” are reproduced.

[0046] In summary, the method of the present invention perfectly realizes 18 multidimensional multiplexing channels, and these 18 channels have been proven by holographic imaging simulation tests. The present invention has very important practical significance for the research on increasing the number of multidimensional multiplexing channels of non-interleaved metasurfaces.

Claims

1. A method for increasing the number of multiplexed channels of a non-interleaved multi-dimensional channel multiplexing metasurface, characterized by: It includes The traditional GS algorithm is optimized using the first-kind Rayleigh-Sommerfeld diffraction formula. This optimization method regards the diffraction process as a response process and extracts the response function from the first-kind Rayleigh-Sommerfeld diffraction formula, and then performs iterative calculations. The ability of meta-atoms on the metasurface to control the light field can be expressed using the Jones matrix To describe it, when the superatom rotates, the Jones matrix becomes Among them: x and Ψ y They are the phase shifts caused by x-polarized light and y-polarized light passing through the superatom with a rotation angle of 0; After processing the target image with the optimized GS algorithm, the phase distribution information required for designing the metasurface can be obtained. Then, the phase distribution information is processed by the Jones matrix and gradient descent method to obtain the phase Ψ related to the specific metaatom. x , Ψ y and the information distribution of the rotation angle θ, and the superatom Ψ x , Ψ y The phase database is compared to obtain the required meta-atom and finally the target meta-surface; The loss function of the gradient descent method is: Δ i is the target light field p i and the calculated light field The difference.

2. The method for increasing the number of multiplexing channels of a non-interleaved multi-dimensional channel multiplexing metasurface according to claim 1, characterized in that: Jones Matrix The elements of the Jones matrix represent polarization channels. To ensure that the energy of each channel is uniform, that is, the amplitude of all channels is the same, the Jones matrix is ​​restricted to Ψ1, Ψ2 and Ψ3 are about Ψ x , Ψ y and the function of the rotation angle θ.

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